$ \left(\dfrac{49}{100}\right)^{-\frac{3}{2}}$
$= \left(\dfrac{100}{49}\right)^{\frac{3}{2}}$ $= \left(\left(\dfrac{100}{49}\right)^{\frac{1}{2}}\right)^{3}$ To simplify $\left(\dfrac{100}{49}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{100}{49}$ To simplify $\left(\dfrac{100}{49}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{10}{7}}\right)^{2}=\dfrac{100}{49}$ so $ \left(\dfrac{100}{49}\right)^{\frac{1}{2}}=\dfrac{10}{7}$ So $\left(\dfrac{100}{49}\right)^{\frac{3}{2}}=\left(\left(\dfrac{100}{49}\right)^{\frac{1}{2}}\right)^{3}=\left(\dfrac{10}{7}\right)^{3}$ $= \left(\dfrac{10}{7}\right)\cdot\left(\dfrac{10}{7}\right)\cdot \left(\dfrac{10}{7}\right)$ $= \dfrac{100}{49}\cdot\left(\dfrac{10}{7}\right)$ $= \dfrac{1000}{343}$